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Theory of Physical and Technical Measurement
1st Edition - March 25, 1992
Author: J. Piotrowski
9 7 8 - 0 - 4 4 4 - 5 9 8 3 3 - 2
A complete theory of measurement from the principles of establishing the reality images to measurement procedures is presented in this book. A precise mathematical model of errors… Read more
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A complete theory of measurement from the principles of establishing the reality images to measurement procedures is presented in this book. A precise mathematical model of errors is presented with the use of various applications to interpret measurement results. Axioms are formulated which provide a deduction theory of measurement. The variety of problems addressed by modern science results in a diversity of models of physical and metrological phenomena, and leads to the view that there is not now, and may never be, a uniform theory of measurement. There is a need, however, to establish a foundation common to all measurements and studies, and this is the author's main aim allied to attempts to create a universal theory of measurement. The purpose of measurement is discussed. Many practical examples illustrating the methodology of modelling, calibration and the analysis of the results of measurement are reviewed. The book is designed for physicists, analytical and physical chemists and engineers involved with the work of metrology. A knowledge of physics, probability and statistics and the principles of metrology is a prerequisite for understanding this work.
1. Establishing Algorithms for the Cognition Process. The logical and formal rules for producing images of reality. Physical scales and the ambiguity of images of reality. Multidimensional scales. 2.Standards and the Propagation of Standards. Establishing the standards of units of measurement. Propagation of standards. Single comparison. n-fold comparison with the same primary standard. m-fold comparison with different standards. n-fold comparison with m different primary standards. m times larger measure of a secondary standard. m times smaller measure of a seocndary standard. The certified reference materials. 3. Modelling of Measurement Systems. The general principles of modelling. Modelling of the characteristics of measurement systems. The static model. Dynamic models. Discrete-time models of measurement systems. The modeling of error sources. Probabilistic models. Nonlinear elements. Dynamic elements. Non-stationary error sources. The general model of error. The continuous-time model. The discrete-time model. The correlation of errors. Identification of models of measurement systems. Determination of the variables of a model. Correlation analysis. Regression analysis. The least squares method. Other methods. 4. The Theory of Error. Images of reality in measurement systems. Principles of image production. Optimization of calibration procedures. Definition and classification of errors. The metrological characteristics of measurement systems and standards. Metrological characteristics. Methodology of their determination and interpretation. Determination of class 1 characteristics. Theoretical determination of the limiting distribution of errors. Experimental determination of the limiting distributions of errors. Interpretation of the concept of accuracy class. The basic concepts of inference in the theory of error. 5. Measurement Procedures. Definition of measurement. Procedures describing measurement methods. Calibration procedures. Reading checking and adjustment of measurement systems. Measurement procedures for constant quantities. Single Measurement. Multiple measurement - the measurement series. Measurement procedures for time-dependent quantities. Single measurement. Multiple measurement. 6. The Design of Measurements and Experiments. Selection of standards for calibration of measuring instruments. Transfer of a measure of a standard onto measuring instruments. Selection of the calibration points. The boundary problems of G-optimum designs. The design principles of calibration processes. Selection of the error sampling interval. Error estimation in a correlated-error measurement series. Total error analysis for a measuring instrument. Appendix. The Lebesgue measure of a set. References. Index.